scholarly journals Nonconnected moduli spaces of nonnegative sectional curvature metrics on simply connected manifolds

2017 ◽  
Vol 50 (1) ◽  
pp. 96-107 ◽  
Author(s):  
Anand Dessai ◽  
Stephan Klaus ◽  
Wilderich Tuschmann
Keyword(s):  
Sectional Curvature ◽  
Moduli Spaces ◽  
Nonnegative Sectional Curvature ◽  
Simply Connected Manifolds ◽  
Simply Connected

scholarly journals Moduli spaces of nonnegative sectional curvature and non-unique souls

2011 ◽  
Vol 89 (1) ◽  
pp. 49-85 ◽  
Author(s):  
Igor Belegradek ◽  
Slawomir Kwasik ◽  
Reinhard Schultz
Keyword(s):  
Sectional Curvature ◽  
Moduli Spaces ◽  
Nonnegative Sectional Curvature

scholarly journals TOPOLOGICAL 4-MANIFOLDS WITH 4-DIMENSIONAL FUNDAMENTAL GROUP

2021 ◽  
pp. 1-8
Author(s):  
DANIEL KASPROWSKI ◽  
MARKUS LAND
Keyword(s):  
Fundamental Group ◽  
Homotopy Equivalent ◽  
Poincaré Duality ◽  
Poincare Duality ◽  
Canonical Map ◽  
Duality Space ◽  
Simply Connected Manifolds ◽  
Simply Connected ◽  
Poincaré Duality Space

Abstract Let $\pi$ be a group satisfying the Farrell–Jones conjecture and assume that $B\pi$ is a 4-dimensional Poincaré duality space. We consider topological, closed, connected manifolds with fundamental group $\pi$ whose canonical map to $B\pi$ has degree 1, and show that two such manifolds are s-cobordant if and only if their equivariant intersection forms are isometric and they have the same Kirby–Siebenmann invariant. If $\pi$ is good in the sense of Freedman, it follows that two such manifolds are homeomorphic if and only if they are homotopy equivalent and have the same Kirby–Siebenmann invariant. This shows rigidity in many cases that lie between aspherical 4-manifolds, where rigidity is expected by Borel’s conjecture, and simply connected manifolds where rigidity is a consequence of Freedman’s classification results.

Stein manifolds of nonnegative curvature

2018 ◽  
Vol 18 (3) ◽  
pp. 285-287
Author(s):  
Xiaoyang Chen
Keyword(s):  
Fixed Point ◽  
Sectional Curvature ◽  
Normal Bundle ◽  
Stein Manifold ◽  
Riemannian Metric ◽  
Nonnegative Curvature ◽  
Fixed Point Set ◽  
Nonnegative Sectional Curvature ◽  
Point Set ◽  
Nonempty Compact

AbstractLet X bea Stein manifold with an anti-holomorphic involution τ and nonempty compact fixed point set Xτ. We show that X is diffeomorphic to the normal bundle of Xτ provided that X admits a complete Riemannian metric g of nonnegative sectional curvature such that τ*g = g.

NEW POLARIZATIONS ON THE MODULI SPACES AND THE THURSTON COMPACTIFICATION OF TEICHMÜLLER SPACE

1998 ◽  
Vol 09 (01) ◽  
pp. 1-45 ◽  
Author(s):  
JØRGEN ELLEGAARD ANDERSEN
Keyword(s):  
Moduli Space ◽  
Moduli Spaces ◽  
Teichmüller Space ◽  
Closed Surface ◽  
Teichmuller Space ◽  
Open Dense Subset ◽  
Complex Structures ◽  
Thurston Boundary ◽  
Simply Connected ◽  
Singular Metric

Given a foliation F with closed leaves and with certain kinds of singularities on an oriented closed surface Σ, we construct in this paper an isotropic foliation on ℳ(Σ), the moduli space of flat G-connections, for G any compact simple simply connected Lie-group. We describe the infinitesimal structure of this isotropic foliation in terms of the basic cohomology with twisted coefficients of F. For any pair (F, g), where g is a singular metric on Σ compatible with F, we construct a new polarization on the symplectic manifold ℳ′(Σ), the open dense subset of smooth points of ℳ(Σ). We construct a sequence of complex structures on Σ, such that the corresponding complex structures on ℳ′(Σ) converges to the polarization associated to (F, g). In particular we see that the Jeffrey–Weitzman polarization on the SU(2)-moduli space is the limit of a sequence of complex structures induced from a degenerating family of complex structures on Σ, which converges to a point in the Thurston boundary of Teichmüller space of Σ. As a corollary of the above constructions, we establish a certain discontinuiuty at the Thurston boundary of Teichmüller space for the map from Teichmüller space to the space of polarizations on ℳ′(Σ). For any reducible finite order diffeomorphism of the surface, our constuction produces an invariant polarization on the moduli space.

scholarly journals Positively curved 6-manifolds with simple symmetry groups

2002 ◽  
Vol 74 (4) ◽  
pp. 589-597 ◽  
Author(s):  
FUQUAN FANG
Keyword(s):  
Sectional Curvature ◽  
Isometry Group ◽  
Symmetry Groups ◽  
Positive Sectional Curvature ◽  
Identity Component ◽  
Simply Connected ◽  
Lie Subgroup ◽  
Positively Curved

Let M be a simply connected compact 6-manifold of positive sectional curvature. If the identity component of the isometry group contains a simple Lie subgroup, we prove that M is diffeomorphic to one of the five manifolds listed in Theorem A.

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